Non-minimal scalar fields in 2D de Sitter and dilaton black holes

We study non-minimal quantum fields in the gravitational field of 2-dimensional dilaton black holes and the de Sitter spacetime. We found that the Green functions for non-minimal massless fields in a particular class of dilaton black holes and in the de Sitter spacetime are almost identical. Using this symmetry exact solutions are derived for quasinormal modes and bound states in these background geometries. The problem of stability of dilaton black holes is discussed.Comment: 12 pages, 4 figure

Minimal surfaces and entanglement entropy in anti-de Sitter space

According to Ryu and Takayanagi, the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We study this holographic geometrical method of calculating the entanglement entropy in the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. Namely, we investigate the minimal surfaces spanned on boundaries of spherical domains at infinity of hyperbolic space, which represents a time-slice of AdS spacetime. We consider a generic position of two spherical domains: two disjoint domains, overlapping domains, and touching domains. In all these cases we find the explicit expressions for the minimal surfaces and the renormalized expression for the area. We study also the embedding of the minimal surfaces into full AdS spacetime and we find that for a proper choice of the static Killing vector we can model a dynamical situation of "tearing" of the minimal surface when the domains on which it is spanned are moved away from each other.Comment: 36 pages, 21 figures, for version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers

Classical self-energy and anomaly

We study the problem of self-energy of pointlike charges in higher dimensional static spacetimes. Their energy, as a functional of the spacetime metric, is invariant under a specific continuous transformation of the metric. We show that the procedure of regularization of this formally divergent functional breaks this symmetry and results in an anomalous contribution to the finite renormalized self-energy. We proposed a method of calculation of this anomaly and presented an explicit expressions for it in the case of a scalar charge in four and five-dimensional static spacetimes. This anomalous correction proves to be zero in even dimensions, but it does not vanish in odd-dimensional spacetimes.Comment: 5 page

Charged particles in higher dimensional homogeneous gravitational field: Self-energy and self-force

A problem of self-energy and self-force for a charged point-like particle in a higher dimensional homogeneous gravitational field is considered. We study two cases, when a particle has usual electric charge and a case when it has a scalar charge, which is a source of a scalar massless minimally coupled field. We assume that a particle is at rest in the gravitational field, so that its motion is not geodesic and it has an acceleration a directed from the horizon. The self-energy of a point charge is divergent and the strength of the divergence grows with the number of dimensions. In order to obtain a finite contribution to the self- energy we use a covariant regularization method which is a modification of the proper time cut-off and other covariant regularizations. We analyze a relation between the self-energy and self-force and obtain explicit expressions for the self-forces for the electric and scalar charge in the spacetimes with the number of dimensions up to eight. General expressions for the case of higher dimensions are also obtained. We discuss special logarithmic factors ln(a), which are present both in the self-energy and self-force in odd dimensions. Finally, we compare the obtained results with the earlier known results both for the homogeneous gravitational field and for particles near black holes.Comment: 43 pages, two subsections added, a few tables and references adde